Extending the Covariant Confined Quark Model to Describe Radial Excitations of Heavy Quarkonia

Abstract

We present an extension of the Covariant Confined Quark Model (CCQM) that enables a consistent description of radial excitations of heavy quarkonia. The conventional CCQM formulation, based on static constituent quark masses, faces a limitation in describing states whose squared mass exceeds the sum of the squared constituent masses. To overcome this, we introduce a running constituent quark mass in the quark loop, allowing an accurate representation of excited hadronic decays. The binding energy of an excited state is assumed equal to that of the corresponding ground state, leading to a simple mass relation between quarkonia and their constituents. Model parameters are determined from experimental data on leptonic decays of charmonia and bottomonia, showing excellent agreement with observations. Furthermore, an orthogonality condition for radial excitations is implemented through modified vertex functions, ensuring that distinct excited states do not mix. This refinement leads to improved internal consistency and predictive power of the CCQM for excited hadronic systems.